6 citations · 9 across the 2 of their papers we have counts for
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Empirical spectral measures of quantum graphs in the Benjamini-Schramm limit
Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri +1
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graph…
Absolutely Continuous Spectrum for Quantum Trees
Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri +1
We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling…
Quantum ergodicity for large equilateral quantum graphs
Maxime Ingremeau, Mostafa Sabri, Brian Winn
Consider a sequence of finite regular graphs (GN) converging, in the sense of Benjamini-Schramm, to the infinite regular tree. We study the induced quantum graphs with equilateral…
Sharp resolvent bounds and resonance-free regions
Maxime Ingremeau
In this note, we consider semiclassical scattering on a manifold which is Euclidean near infinity or asymptotically hyperbolic. We show that, if the cut-off resolvent satisfies pol…